Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Segmental bioelectrical impedance analysis to assess perioperative fluid changes.

OBJECTIVES: Perioperative fluid accumulation determination is a challenge for the clinician. Bioelectrical impedance analysis (BIA) is a noninvasive method based on the electrical properties of tissues, which can assess body fluid compartments. The study aimed at assessing their changes in three types of surgery (thoracic, abdominal, and intracranial) requiring various regimens of fluid administration. DESIGN: Prospective descriptive trial. PATIENTS: A total of 26 patients scheduled for elective surgery were separated into three groups according to site of surgery: thoracic (n = 8), abdominal aortic (n = 8), and brain surgery (n = 10). SETTING: University teaching hospital. INTERVENTION: None. MEASUREMENTS: Whole body, segmental (arm, trunk, and legs) BIA at multiple frequency (0.5, 50, 100 kHz) was used to assess perioperative fluid accumulation after surgery. The fluid balances were calculated from the charts. RESULTS: The patients were aged 62+/-4 yrs. Fluid balances were 4.8+/-1.0 L, 4.1+/-0.5 L, and 1.9+/-0.3 L, respectively, in the three groups. In trunk surgery patients, fluid accumulation was detected as a drop in impedance in the operated area at all frequencies. In the operated area, there was an expansion of both intra- and extracellular compartments. A reduction in high frequencies' impedance in the legs was only detected after aortic surgery. Fluid accumulation and trunk impedance changes were strongly correlated. Neurosurgery only induced minor body fluid changes. CONCLUSIONS: Segmental BIA is able to detect and localize perioperative fluid accumulation. It may become a bedside tool to quantify and to localize fluid accumulation.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

Reproducibility and within-day variability of body fat measurements using segmental bipolar bioelectrical impedance in women

BACKGROUND AND AIMS: little is known regarding the reproducibility of body fat measuring devices; hence, we assessed the between and within-device reproducibility, and the within-day variability of body fat measurements. METHODS: body fat percentage was measured twice on seventeen female students aged between 18 and 20 with a body mass index of 21.9 ± 2.5 kg/m2 (mean ± SD) using seven bipolar bioelectrical impedance devices. Each participant was also measured each hour between 7:00 and 22:00. RESULTS: the correlation between first and second measurements was very high (Spearman r between 0.985 and 1.000, p<0.001), as well as between devices (Spearman r between 0.916 and 0.991, p<0.001). Repeated measurements analysis showed no differences were between devices (p=0.59) or readings (first vs. second: p=0.74). Conversely, significant differences were found between assessment periods throughout the day, measurements made in the morning being lower than those made in the afternoon (F test for repeated values= 6.58, p<0.001). CONCLUSIONS: the between and within-device reproducibility for measuring body fat is high, enabling the use of multiple devices in a single study. Conversely, small but significant changes in body fat measurements occur during the day, urging body fat measurements to be performed at fixed times.

Segmental body composition assessed by bioelectrical impedance analysis and DEXA in humans.

The present study assessed the relative contribution of each body segment to whole body fat-free mass (FFM) and impedance and explored the use of segmental bioelectrical impedance analysis to estimate segmental tissue composition. Multiple frequencies of whole body and segmental impedances were measured in 51 normal and overweight women. Segmental tissue composition was independently assessed by dual-energy X-ray absorptiometry. The sum of the segmental impedance values corresponded to the whole body value (100.5 +/- 1.9% at 50 kHz). The arms and legs contributed to 47.6 and 43.0%, respectively, of whole body impedance at 50 kHz, whereas they represented only 10.6 and 34.8% of total FFM, as determined by dual-energy X-ray absorptiometry. The trunk averaged 10.0% of total impedance but represented 48.2% of FFM. For each segment, there was an excellent correlation between the specific impedance index (length2/impedance) and FFM (r = 0.55, 0.62, and 0.64 for arm, trunk, and leg, respectively). The specific resistivity was in a similar range for the limbs (159 +/- 23 cm for the arm and 193 +/- 39 cm for the leg at 50 kHz) but was higher for the trunk (457 +/- 71 cm). This study shows the potential interest of segmental body composition by bioelectrical impedance analysis and provides specific segmental body composition equations for use in normal and overweight women.

Cross-validation of bioelectrical impedance analysis for the assessment of body composition in a representative sample of 6- to 13-year-old children.

BACKGROUND/OBJECTIVES: (1) To cross-validate tetra- (4-BIA) and octopolar (8-BIA) bioelectrical impedance analysis vs dual-energy X-ray absorptiometry (DXA) for the assessment of total and appendicular body composition and (2) to evaluate the accuracy of external 4-BIA algorithms for the prediction of total body composition, in a representative sample of Swiss children. SUBJECTS/METHODS: A representative sample of 333 Swiss children aged 6-13 years from the Kinder-Sportstudie (KISS) (ISRCTN15360785). Whole-body fat-free mass (FFM) and appendicular lean tissue mass were measured with DXA. Body resistance (R) was measured at 50 kHz with 4-BIA and segmental body resistance at 5, 50, 250 and 500 kHz with 8-BIA. The resistance index (RI) was calculated as height(2)/R. Selection of predictors (gender, age, weight, RI4 and RI8) for BIA algorithms was performed using bootstrapped stepwise linear regression on 1000 samples. We calculated 95% confidence intervals (CI) of regression coefficients and measures of model fit using bootstrap analysis. Limits of agreement were used as measures of interchangeability of BIA with DXA. RESULTS: 8-BIA was more accurate than 4-BIA for the assessment of FFM (root mean square error (RMSE)=0.90 (95% CI 0.82-0.98) vs 1.12 kg (1.01-1.24); limits of agreement 1.80 to -1.80 kg vs 2.24 to -2.24 kg). 8-BIA also gave accurate estimates of appendicular body composition, with RMSE < or = 0.10 kg for arms and < or = 0.24 kg for legs. All external 4-BIA algorithms performed poorly with substantial negative proportional bias (r> or = 0.48, P<0.001). CONCLUSIONS: In a representative sample of young Swiss children (1) 8-BIA was superior to 4-BIA for the prediction of FFM, (2) external 4-BIA algorithms gave biased predictions of FFM and (3) 8-BIA was an accurate predictor of segmental body composition.

Reproducibility and within-day variability of body fat masurements using segmental bipolar bioelectrical impedance in women

Objective: to assess the between and within-device reproducibility, as well as within-day variability of body fat measurements. Methods: body fat percentage (%BF) was measured twice on seventeen female students aged between 18 and 20 with a body mass index of 21.9 22.6 kg/m2 (mean SD) using seven bipolar bioelectrical impedance devices (BF-306) according to the manufacturer's recommendations. Each student was also measured each hour between 7:00 and 22:00. Statistical analysis was conducted using a general linear model for repeated measurements. Results: the correlation between first and second measurements was very high (Pearson r between 0.985 and 1.000, p<0.001), as well as the correlation between devices (Pearson r between 0.986 and 0.999, all p<0.001). Repeated measurements analysis showed no differences were between devices (F test=0.83, p=0.59) or readings (first vs. second: F test=0.12, p=0.74). Conversely, significant differences were found between assessment periods throughout the day, measurements made in the morning being lower than those made in the afternoon. Assuming an overall daily average of 100 (based on all measurements), the values were 95.8 3.2 (mean SD) at 8:00 versus 101.3 3.0 at 20:00, corresponding to a mean change of 2.2 1.1 in %BF (F test for repeated values=6.58, p<0.001). Conclusions: the between and within-device reproducibility for measuring body fat is high, enabling the use of multiple devices in a single study. Conversely, small but significant changes in body fat measurements occur during the day, urging body fat measurements to be performed at fixed times.

Estimation of zero-sequence impedance of undergrounds cables for single-phase fault location in distribution systems with electric arc

This paper focus on the problem of locating single-phase faults in mixed distribution electric systems, with overhead lines and underground cables, using voltage and current measurements at the sending-end and sequence model of the network. Since calculating series impedance for underground cables is not as simple as in the case of overhead lines, the paper proposes a methodology to obtain an estimation of zero-sequence impedance of underground cables starting from previous single-faults occurred in the system, in which an electric arc occurred at the fault location. For this reason, the signal is previously pretreated to eliminate its peaks voltage and the analysis can be done working with a signal as close as a sinus wave as possible

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method